Question

A two-digit number is such that the product of its digits is 12.When 36 is added To This number,the digits interchange their places.
Find Number.
(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)

Answer 1

SOLUTION:

Let the two digit number =10x + y

Given, the product of its digits(xy) = 12

xy = 12...................(1)

when 36 is added to the number, the digits interchange their places

10x + y+36 = 10y + x

10x + y - 10y - x = -36

9x - 9y = -36

9(x - y) = -36

x - y = -36/9

x - y = - 4


x= -4+y……………….(2)


Put this value of x in eq 1.


xy=12


(-4+y)y = 12


-4y+y²=12


y²-4y-12=0


y²-6y+2y-12=0


y(y-6)+2(y-6)=0


y-6=0


y=6


y+2=0


y=-2 (y cannot be negative)


Hence , y = 6


Put this value of y in eq 1


xy=12


x× 6= 12


x= 12/6=2


x=2


Required number= 10x+y


= 10(2)+6


= 20 +6


Required number= 26


Hence, the Required number is 26.


Hope this will help you....

Answer 2

26 is the ans 2into 6 =12 and 26+36=62